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An iterative procedure is proposed to determine the far-field state of stress that exists in a rock mass with non-linear behavior around a tunnel. Absolute displacements of the tunnel wall obtained by means of geodetic measurements are used to identify the boundary stress conditions. Previous information is accounted for, so that boundary conditions can be updated at the various stages of a project, as soon as new information becomes available. The application to the 2-D plane strain synthetic model of a tunnel in a yielding rock mass shows the fast convergence of the procedure and the need to use absolute displacements (rather than relative displacements) in order for the identification problem to be well-posed.